I received a Form 1099-G, regarding a payment received during the year, for my state tax refund. Do I have to include this amount as income on my
return?

Whether or not you have to report your state income tax refund on your federal income tax return depends on if you itemized your deductions using
Schedule A (Form 1040) (PDF):

If you did not itemize your deductions on your federal tax return for the same year to which the state or local tax refund applies, do not report any of the refund as
income.

If you received a refund of state or local income taxes this year for which you took an itemized deduction in an earlier year, you may have to include all or part of the refund as income on your tax
return.

Report your taxable state or local refunds on line 10 of
Form 1040 (PDF). You cannot use
Form 1040A (PDF) or
Form 1040EZ (PDF) if the item must be reported on your return.